Lorentz spaces in action on pressureless systems arising from models of\n collective behavior

2020/05/12 by Raphaël Danchin, Danchin, Raphaël, Piotr B. Mucha +3 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2005.05603

Abstract

We are concerned with global-in-time existence and uniqueness results for\nmodels of pressureless gases that come up in the description of phenomena in\nastrophysics or collective behavior. The initial data are rough: in particular,\nthe density is only bounded. Our results are based on interpolation and\nparabolic maximal regularity, where Lorentz spaces play a key role. We\nestablish a novel maximal regularity estimate for parabolic systems in\nL_q,r(0,T;L_p(\Ω)) spaces.\n

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• Fujita-Kato solution for the 3D compressible pressureless Navier-Stokes equations with discontinuous and large-variation density

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